Permutation decoding of Z2Z4-linear codes

TL;DR

The paper introduces a permutation decoding method applicable to any binary systematic code, including nonlinear Z2Z4-linear codes, demonstrated on Hadamard Z2Z4-linear codes, expanding decoding options for these codes.

Contribution

It presents a new permutation decoding approach that works for both linear and nonlinear binary codes, specifically applied to Z2Z4-linear codes.

Findings

Decoding method applicable to nonlinear codes

Successfully applied to Hadamard Z2Z4-linear codes

Proved systematic encoding exists for these codes

Abstract

An alternative permutation decoding method is described which can be used for any binary systematic encoding scheme, regardless whether the code is linear or not. Thus, the method can be applied to some important codes such as Z2Z4-linear codes, which are binary and, in general, nonlinear codes in the usual sense. For this, it is proved that these codes allow a systematic encoding scheme. As a particular example, this permutation decoding method is applied to some Hadamard Z2Z4-linear codes.